A has another sum as hand-written and 32/13 is of course not bigger than 24 ... then: in the last sequence C: the difference between 2 and 6 is 4, so 2 and 6 are more different than 7 and 10, why 7 and 10 have been selected?

The point i wanted to make was to catch all the numbers that were the smallest numbers of a serie but that were common to each serie presented in the three series above and the three smalest number that were different from each serie of numbers(minimum common difference ) and then make up a new seried of numbers with those characteristics.Forget my example because i started simulating numbers ( elements ) to try to catch the least common number different from each serie but the programing ( lines of program ) came out completely odd from what i supposed, i think you have to start different from me.

Well, if one considers test input a0, a1, a2 as series and some substructure in a given series as succession and defines a succession as a list of consecutive elements with constant difference between sucession members, the following arises:

Hi Udo, great, albeit somewhat complex. I wanted to show the single steps. Moreover I think it suffices to look at all pairs of subsets of cp, and it is not neccesary to look at all subsets of cp with more elements than 2. This would save time and memory. So I think one could write as well

The empty sets could indeed be an issue indicating that there are elements which don't occur in some of the original sets after removing the elements common to all sets. Perhaps you could include an error-variable ( perhaps Catch, Throw ?) in your 2-liner?

are identical
$A_2 \equiv A_{23}$, which is clear because of the
$\vee$ (logical OR) and the fact, that intersections of three sets are not more permissive as intersections of two sets. Actually I was driven by your other remark

Now again find elements in cp common to all members in cp comparing
all subsets

to deliver a generic code sample which could deliver all subsets. It was restricted to the subsets with
$2,3,...,n-1$ members and should be restricted even more in the given context, as you say.

I just would like to thank you all for coming out with a solution for the puzzle I presented , i think you are all top mathmaticians and programmers. Now i am using it to take the pixels that are least common and and least ifferent form 2 pictures. I think all you know how important it is to take out the sequences a it applies to many areas of imaging. Unfortunately i do not know how to apply it tomodifying image pixels so that i get an image from imagelevels or image data.